The previous counting methods trained by the density map regression scheme fail to precisely count the number of birds in crowded bird images of various scales. This is due to the coarseness of the manually created target density maps. In this paper, we propose a new counting scheme, called DAM counting, which generates our-first-proposed density activation map (DAM). DAM is a CNN perspective density map that has high activation values where the network focuses on for precise counting of birds. The network is trained to autonomously learn where and how much the DAM should be activated so that the sum of all values in the DAM estimates the number of birds. Moreover, our DAM counting scheme incorporates two segmentation regularizers that enable precise counting of birds with various scales and appearance. Our DAM counting scheme can effectively substitute the existing density map regression scheme, bringing in a remarkable increase of 45% in the counting accuracy. We also propose the first crowded bird dataset, called CBD-6000, which is very valuable for crowded bird counting research.